Quite the opposite. You can easily get a state of the art LLM to do a complete 180 on its entire moral framework with a few words injected in the prompt (and this very example demonstrates exactly that). It is very far from logically or ethically consistent. In fact it has no logic and ethics at all.

Though if we did get an AI priest it would be great to absolve all your sins with some clever wordplay.

Haha exactly. Except when it agrees with my political preferences on something. In that case, the LLM is just betraying its deep internal consistency and lack of hypocrisy.